Textbook in PDF format This is a different kind of class and math book. You may be used to mathematics where you compute something, whether you solved an equation, differentiated a function, simplified an expression, determined a limit, or evaluated an integral. You may have worked on applying theorems (such as the Squeeze Theorem for limits) and have built strategies for a certain problem type (sorting out when to integrate using substitution versus when to integrate by parts). The majority of your mathematical experience so far may have been computational in nature. However, when you rely on theorems from calculus, how do you know that what you rely upon is solid? If this text is in front of you, it is because you are now at a place in your mathematical career where computation can be put aside for a moment so that you can learn how to read and write mathematical proofs. Saying the word “proof” may sound scary to you. In fact, due to previous experiences, you may have some extremely negative feelings associated to proofs. In the past, you may have dealt with ε-δ proofs in a first semester calculus class. You may have preferred computing derivatives of functions over applying the Squeeze Theorem, the Intermediate Value Theorem, or the Mean Value Theorem. Applying convergence tests for infinite series may have seemed like such a strange experience in calculus. The portions of a class where you were expected to “do proofs” may have been “coached” in the following sense: you “knew” when an exam question needed the Intermediate Value Theorem and you could even apply the theorem for full credit, but you never quite felt sure about what you were doing. If that resonates with you, then this handbook should be really refreshing. As a student who has taken at least a semester of calculus, you’re now at a stage where a complete foundation in mathematical proof can and should be discussed. There is a complete framework that needs to be learned. If you’re reading this, someone gave you this text with the confidence that you have the background and technical skills to learn this complete framework. (If you’re discovering this text on your own, successful completion of one semester of calculus is about the right level of experience for reading this text.)